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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Instead of being surrounded by fancy rings, today's unusual midget is surrounded by fragments, which at a quick glance resemble butterflies. I think the insect was long ago called a flutterby, but the original descriptive word somehow got changed to the much-less-sensible word, butterfly. But regardless of where the name came from, the fluttering lepidoptera are in the picture, and they appear to be coming closer, justifying the name "Butterflies Coming". Whether the rating of 6 is fair, stingy or generous is up to the viewer to decide. The parent fractal results when 51 parts of Z^2.49 are subtracted from 51 parts of Z^2.51 before adding C, and Z is initialized to a critical value. This parent resembles the fractal produced by the formula Z^3.05+C, with a double main bay with East-type Valleys on both the east and west sides. Today's scene lies in a chaotic area on the south side of the west valley, which is beginning to split. With its render time of under 3 minutes, running the attached parameter file is a rather efficient way of seeing the floating fractal butterflies. A slightly more efficient way is to give Paul and Scott a chance to render and post the image, and then to download it from one of their sites. Paul's site is at: The fractal weather today here at FC was partly cloudy with a temperature of 84F 29C. The cats, who enjoy such ideal conditions, took advantage of the day's weather by spending several hours in the yard. Tippy, the tabby, interrupted his enjoyment by chasing off an intruding cat, while Thomas, the oversized yellow-orange one, watched with interest. It's now time to do the things that need to be done, so until next time, take care, and when the impossible happens, it never was impossible in the first place. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Butterflies_Coming { ; time=0:02:40.60--SF5 on a p200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=-0.145097748537010/-0.03306885818455196\
/62417.47/1/155 params=51/2.51/-51/2.49/0/0 float=y
maxiter=400 inside=0 logmap=27
colors=000PdvSduUdsXdr_dqcdofdnhdmjdlkemlgnnioojoq\
lprnqtprurrwssxutyvtxvpwumvtjvsgurdtrasqZspWroTqnQ\
pnNpmKolHnkEmjBmj8jg7he7eb7c`7`Y7ZW6WT6UR6RO6PM6QL\
8RLASLCTKEUKGVKIWJKXJMYJOZIQ_IS`IUaHWbHYcH_bIZbIYb\
JXbJWbJVaKVaKUaKTaLSaLRaLRZNPWPNURLRTKPVIMXGJZFH`D\
EbBCcABdCBeEBfGAfIAgKAhMAhN9iP9jR9kT8kV8lX8mZ8m_Eq\
YKuWQxUWzSazQfzPhzSiwUjqWkkYle_m_anUcUiO9y88vB8sD8\
pF8nI8kK8hM8fOCeRFdUIcXMbZPbaSadV`gZ_iaZlzZozYrzXt\
zWwzVzzVzzczzlzztzzqxznwzkuzitUfrUcqU`ozZnzWlzTkzQ\
izOhziXzfWzcWzaWzZWzWWzUWzRWzPWzMWzJWzHWzEWzCWzMcz\
Wjzeqzoxznwznvznuznuzntznsznsznrzmqzmqzmpzmozmozmn\
zmmzmmzonzpozqozrpzspztqzvrzwrzxszyszztzztzzuzzvzz\
wzzxzzyzzzzzzzzzzzzzxzzrxzlwzfuz`szWrzZkzadzcYzfRz\
hKzJFzIIzIKzHMzHOzHQzGTzGVzFXzFZzF`zEczEezDgzDizDk\
zQlzblzdbzfUzhLzjCzhGzgKzfNzeRzdUzcYzaaz`dz_hzZkzY\
ozXrzWqzWqzezzdzzdzzdyzdw
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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